一种局部多项式时空地理加权回归方法

doi:10.11947/j.AGCS.2018.20170674

测绘学报 ›› 2018, Vol. 47 ›› Issue (5): 663-671.doi: 10.11947/j.AGCS.2018.20170674

• 中国测绘地理信息学会2017年青年优秀论文 • 上一篇下一篇

一种局部多项式时空地理加权回归方法

赵阳阳¹, 张小璐¹, 张福浩¹, 仇阿根¹, 杨毅², 石丽红¹, 刘晓东¹

1. 中国测绘科学研究院政府地理信息系统研究中心, 北京海淀 100830;
2. 淮海工学院测绘与海洋信息学院, 江苏连云港 222000

收稿日期:2017-11-28 修回日期:2018-03-12 出版日期:2018-05-20 发布日期:2018-06-01
通讯作者: 张小璐 E-mail:397203228@qq.com
作者简介:赵阳阳(1987-),女,博士,助理研究员,研究方向为时空数据分析与挖掘。E-mail:nhyyangyang@126.com
基金资助:
国家重点研发计划（2016YFC0803101）；中国测绘科学研究院基本科研业务费（7771812）

A Local Polynomial Geographically and Temporally Weight Regression

ZHAO Yangyang¹, ZHANG Xiaolu¹, ZHANG Fuhao¹, QIU Agen¹, YANG Yi², SHI Lihong¹, LIU Xiaodong¹

1. Chinese Academy of Surveying and Mapping, Research Center of Government Geographic Information System, Beijing 100830, China;
2. School of Geomatics and Marine Information, Huaihai Institute of Technology, Lianyungang 222000, China

Received:2017-11-28 Revised:2018-03-12 Online:2018-05-20 Published:2018-06-01
Supported by:
The National Key Research and Development Program of China (No.2016YFC0803101);The Basic Scientific Research of Chinese Academy of Surveying and Mapping (No.7771812)

摘要/Abstract

摘要： 基于加权最小二乘估计的时空地理加权回归方法，在随机项方差相同且最小的假设条件下估计回归参数和拟合值，由于没有考虑时空分析中异方差影响而导致估计结果存在一定偏差。局部多项式估计是一种消除异方差影响的非参数估计方法。本文在局部多项式估计原理基础上，提出了局部多项式时空地理加权回归方法。它是采用三元一阶泰勒级数展开式重构时空回归系数和自变量矩阵，进而建立满足高斯-马尔可夫独立同分布假定要求的新模型，利用新模型回归系数估计值、拟合值以及新模型与原模型的关系，可得到原模型回归系数估计值和拟合值。本文采用模拟数据和真实数据进行试验，以GTWR与局部线性地理加权回归作为对比方法，从方法适用性、整体估计效果、回归系数估计偏差和拟合优度、整体估计偏差等方面分析了LPGTWR方法性能，有效证明了LPGTWR方法能消除异方差影响提升估计精度。

关键词: 时空地理加权回归, 加权最小二乘估计, 局部多项式, 泰勒级数

Abstract: Geographically and temporally weight regression (GTWR) estimates regression coefficients and fitted value by weighted least squares (WLS), which under the assumption of the same minimum random variance. As without considering the spatio-temporal heteroscedasticity, it may reduce the accuracy of estimation. Local polynomial estimation is a nonparametric estimation method to eliminate heteroscedasticity in statistics. On the basis of the local polynomial estimation, the local polynomial geographically and weight regression temporally (LPGTWR) approach is proposed in this paper. It reconstructs the spatio-temporal coefficients using three-dimensional Taylor Series in order to satisfy the Gauss-Markov assumption of independent identical distribution. Then estimate the regression coefficients and fitting value using weighted least squares. The experiments use both simulated data and real data to compare LPGTWR, GTWR and local linear-fitting-based geographically weight regression (LGWR). Experiments using simulated data showed that LPGTWR can significantly improve the accuracy of estimation not only in goodness-of-fit of the fitted value, but also in reducing bias of the coefficient estimation and the estimation. It is useful by adopting LPGTWR to eliminate heteroscedasticity effect and improve estimation accuracy.

Key words: geographically and temporally weighted regression, weighted least squares, local polynomial, Taylor series

中图分类号:

赵阳阳, 张小璐, 张福浩, 仇阿根, 杨毅, 石丽红, 刘晓东. 一种局部多项式时空地理加权回归方法[J]. 测绘学报, 2018, 47(5): 663-671.

ZHAO Yangyang, ZHANG Xiaolu, ZHANG Fuhao, QIU Agen, YANG Yi, SHI Lihong, LIU Xiaodong. A Local Polynomial Geographically and Temporally Weight Regression[J]. Acta Geodaetica et Cartographica Sinica, 2018, 47(5): 663-671.

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一种局部多项式时空地理加权回归方法

A Local Polynomial Geographically and Temporally Weight Regression

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